MSE 335 Problem Set 1. Due Monday January 30, 2017.
1. A set of data for a particular chemical reaction for the reduction of the partial
pressure, p, of a component with time appears in the table below.
Time (seconds)
Pressure (Pa)
0
8.20
1000
5.72
2000
3.99
3000
2.78
4000
1.94
The value of the pressure at t = 0 corresponds to the initial pressure of the
component in the system. In the first few pages of Lecture 1 we discussed the
kinetics associated with first and second order reactions. Using the data in the
table above determine whether the decomposition of the pressure corresponds to a
1st or 2nd order reaction and determine the rate constant.
2. The rate of a 2nd order decomposition process, k (in units of Lmol-1 s-1), as a
function of temperature is given in the data table below.
T(K)
K
-1 -1
(Lmol s )
700
0.011
730
0.035
760
0.105
790
0.343
810
0.789
840
2.17
910
20.0
1000
145
Determine the activation energy for the decomposition reaction and the attempt
frequency. Be sure to provide the units!
3. The thermal decomposition of an organic nitrile produced the following data.
Time (s)
Nitrile
-1
(Mol-L )
0
1.1
2000
0.86
4000
0.67
6000
0.52
8000
0.41
10000
0.32
12000
0.25
∞
0
Determine the order of the reaction and the rate constant.
4. Calculate the self-diffusivity for the following list of metals at a homologous
temperature of 0.95 based on the given values of Do and the activation energy Q.
Element
Aluminum
Copper
Gold
Lithium
Nickel
Niobium
Sodium
Silver
Tantalum
Vanadium
2
Do (cm /s)
0.047
0.16
0.04
0.038
0.92
0.008
0.004
0.04
0.018
0.014
Q (eV/atom)
1.28
2.07
1.76
0.521
2.88
3.62
0.365
1.76
4.07
2.93
5. The Noyes-­‐Whitney equation is often used to predict the rate at which a solid substance dissolves into water. One form of this equation is: dC
= k Cs − C
dt
where . DA
k=
Vh
Here D is the diffusivity of the dissolving substance in the electrolyte, A is the area of the sample dissolving, h is the thickness of the diffusion boundary layer, V is the volume of electrolyte, C is the time-­‐dependent concentration of the substance in the electrolyte and Cs is the saturation concentration of the substance in the electrolyte. This is equation is often used in the pharmaceutical industry to predict the kinetics of drug release. At 20 °C acetylsalicylic acid (aspirin) has a solubility, Cs = 2 mg/mL. Consider a tablet of aspirin in the form of a disk, 0.4cm in diameter and 0.1cm thick. A. Determine the time-­‐dependent dissolution rate of aspirin at 20 °C in a total volume of water of 5 mL using the following parameter values. Plot your results for dC(t)/dt versus t. B. Determine the time-­‐dependent concentration of dissolved aspirin. Plot your results for C(t) versus t. Does the dissolved aspirin ever reach saturation and if so when? Molecular mass of aspirin =180 g/mol. Density of aspirin = 1.4 g/cm3 D = 10-­‐6 cm2/sec h = 0.01 cm. (
)